Question

find the value of X + Y if if 2 X + 3 Y is equals to 6 and 3 X + 2 Y is equals to 4 ​

Answer 1

Answer :-

→ x + y = 2

To Find :-

→ x + y

Solution :-

Given that ;

→ 2x + 3y = 6 .....eq.(1)

and

→ 3x + 2y = 4 .....eq.(2)

Method (1) Simple

Add these Equation

→ 5x + 5y = 10

→ 5( x + y ) = 10

→ x + y = 5

Method (2)

from eq.(1)

→ 3y = 6 - 2x

$\to \sf{ y = \frac{6 - 2x}{3} } \\ \sf{put \: this \: in \: eq.(2)} \\ \\ \implies \sf{3x + 2 \times \frac{6 - 2x}{3} = 4} \\ \\ \sf{ \implies \: \frac{9x + 12 - 4x}{3} = 4} \\ \\ \implies \sf{ 5x + 12 = 12} \\ \\ \implies \boxed{\sf{ x = 0}} \: \:$

now we have

$\implies \sf{ y = \frac{6 - 2x}{3}} \\ \\ \implies \sf{y = \frac{6}{3} \: \: \because \: x = 0} \\ \\ \implies \boxed{\sf{y = 2 }}$

hence ,

→ x + y = 0 + 2 = 2

Answer 2

$(2x + 3y = 6) \times3 \\ 6x + 9y = 18...........(1) \\( 3x + 2y = 4) \times 2 \\ 6x + 4y = 8.............(2) \\ subtracting \: (2) \: from \: (1) \\ 6x + 9y = 18 \\ 6x + 4y = 8 \\ - \: \: \: \: - \: \: \: \: - \: \: (sign \: change \: and \: we \: get) \\ 0 + 5y = 10 \\ y = 2 \\ 2x + 3y = 6 \: ( \: using \: y = 2) \\ 2x + 3 \times 2 = 6 \\ 2x = 6 - 6 \\ 2x = 0 \\ x = \frac{0}{2} \\ x = 0$

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